Problem: Simplify the following expression: ${-5(9+4z)-(9z-3)}$
Solution: Distribute the ${-5}$ into the first set of parentheses: $ {-5(}\gray{9+4z}{)} - (9z-3) $ $ {-45-20z} - (9z-3) $ The minus sign in front of the parentheses means we multiply each term inside the parentheses by ${-1}$ $ -45-20z {-1(}\gray{9z-3}{)} $ $ -45-20z {-9z+3} $ Rewrite the expression to group the ${z}$ terms and numeric terms: $ {-20z - 9z} {-45 + 3}$ Combine the ${z}$ terms: $ {-29z} {-45 + 3}$ Combine the numeric terms: $ {-29z} {-42}$ The simplified expression is $-29z-42$